Certain groups of asteroids have elliptical orbits that cross the orbit of the
Earth and other inner planets. Thus, these asteroids can come very close to
the Earth. This provides a rationale to study such asteroids beyond the merely
scientific one.

The Earth-Crossing Asteroid 1995 CR

The adjacent animation illustrates the orbit of asteroid 1995 CR,
which was only discovered in 1995. The animation covers the two years---February 3, 1994 through February 3, 1996---at
approximately 1 month intervals, except near the time of discovery (February 3,
1995) where the interval is about 10 days.

This asteroid is of a relatively rare type with an orbital period much faster
than that of the Earth. Notice that its orbit crosses the orbit of all 4 of
the inner planets (though not obvious here, the orbit is almost in the plane of
the ecliptic). On February 22, 1995 (2 1/2 weeks after discovery), this
asteroid passed within 7.5 million km of the Earth---a distance only 20 times
that of the distance to the Moon (note that in the animation the sizes of the
planetary disks and of the asteroid are greatly exaggerated).

Notice how rapidly the asteroid moves on the inner part of its orbit (Kepler's
2nd Law). It covers approximate half of the distance around its orbit in only
about 2 months when it is near the Sun!
Here is the
Present Position
of the asteroid 1995 CR.

Other Earth-Crossing Asteroids

There are a many other known asteroids that cross Earth's orbit (about 300
have been indentified
at present). Here is a
general information source on Near Earth Objects (NEOs) and here is a
listing
of asteroids that come near the Earth and their orbital elements (the
orbital elements allow
their orbit to be plotted with the
Solar System Live software). Here is an
information leaflet from the Royal Greenwich Observatory
summarizing close approaches and comets and asteroids to the Earth in recent
years.
Here are some
predicted close
approaches of asteroids from now until the year 2020. The good news is
that none of these will strike the Earth. The bad news is that we probably
have discovered only a fraction of the total number of Earth-crossing
asteroids, so there are many for which we do not know the orbit. One estimate
is that
the entire population of Earth-crossing asteroids
includes some 1500
larger than one kilometer and 135,000 larger than 100 meters in diameter.

One such Earth-crossing asteroid is Toutatis, which was discussed in the
preceding section.
Its eccentric, four-year orbit
extends from just inside the
Earth's orbit to the main asteroid belt, and the
plane of
Toutatis' orbit lies closer
to the plane of the Earth's orbit than any other Earth-crossing
asteroid presently known.
On September 29, 2004, Toutatis will pass by the Earth at a distance of only
4 times the distance to the Moon---the closest approach to Earth of
any known asteroid or comet between now and 2060. The
asteroid's frequent
close approaches to Earth render its orbit chaotic, so that
its trajectory more than several centuries
into the future cannot be
predicted accurately
(Ref).